Problem: Mr. Bray prepares a list of $43$ US presidents, $8$ of whom died in office. Then $18$ of his students each select a president at random (there can be repeats) for their creative writing assignments. What is the probability that at least one of the students select a president who died in office? Round your answer to the nearest hundredth. $P(\text{at least one death})=$
Answer: Strategy In this situation it is much easier to calculate the probability of the event we are looking for (at least one president who died in office) by calculating the probability of its complement (no presidents who died in office), and subtracting from $1$. In other words, we can use this strategy: $P(\text{at least one death})=1-P(\text{all 18 presidents live})$ Calculations $\begin{aligned} &\phantom{=}P(\text{at least one death}) \\\\ &=1-P(\text{all 18 presidents live}) \\ \\ &=1-\left(\dfrac{35}{43}\right)^{18} \\ \\ &\approx 1-0.0246 \\ \\ &\approx 0.98\end{aligned}$ Answer $P(\text{at least one death}) \approx 0.98$